1. Physics 218, Lecture IXX1 Physics 218 Lecture 19 Dr. David Toback

2. Physics 218, Lecture IXX2 Schedule Changes Please see the handout for schedule changes New Exam 3 Date: Exam 3 Tuesday Nov. 26th

3. Physics 218, Lecture IXX3 Angular Quantities Last time: Position  Angle  Velocity  Angular Velocity  Acceleration  Angular Acceleration  This time move forward on the others: –Force –Mass –Momentum –Energy

4. Physics 218, Lecture IXX4

5. 5 Angular Velocity and Acceleration Are  and  vectors?  and  clearly have magnitude Do they have direction?

6. Physics 218, Lecture IXX6 Right-Hand Rule Yes! Define the direction to point along the axis of rotation Right-hand Rule This is true for  and 

7. Physics 218, Lecture IXX7 Angular Quantities Position  Angle  Velocity  Angular Velocity  Acceleration  Angular Acceleration  Moving forward: –Force –Mass –Momentum –Energy

8. Physics 218, Lecture IXX8 Torque Torque is the analogue of Force Take into account the perpendicular distance from axis –Same force further from axis leads to more Torque

9. Physics 218, Lecture IXX9 Slamming a door We know this from experience: –If we try to slam a door really hard, we grab it at the end –If we try to push in the middle, we aren’t able to make it slam nearly as hard.

10. Physics 218, Lecture IXX10 Torque Continued What if we change the angle at which the Force is applied? What is the “Effective Radius?”

11. Physics 218, Lecture IXX11 Slamming a door We know this also from experience: –If we try to slam a door really hard, we grab it at the end and “throw” perpendicular to the hinges –If we try to pushing towards the hinges, the door won’t even slam.

12. Physics 218, Lecture IXX12 Torque Torque is our “slamming” ability Write Torque as   = RFsin  (We’ll get to the real definition soon enough)

13. Physics 218, Lecture IXX13 Torque and Force Torque problems are like Force problems Sum up all the Torques to find the total torque Is torque a vector?

14. Physics 218, Lecture IXX14 Example: Composite Wheel Two forces, F 1 and F 2, act on different radii of a wheel, R 1 and R 2, at different angles  1 and  2.  1  is a right angle. If the axis isn’t fixed, what happens? If the axis is fixed, what is the net Torque on the wheel? F1F1 F2F2  

15. Physics 218, Lecture IXX15 Angular Quantities Position  Angle  Velocity  Angular Velocity  Acceleration  Angular Acceleration  Moving forward: –Force  Torque  –Mass –Momentum –Energy

16. Physics 218, Lecture IXX16 Analogue of Mass The analogue of Mass is called Inertia Example for a ball of mass m moving in a circle around a point What about lots of points? For example a Wheel.

17. Physics 218, Lecture IXX17 Torque and Moment of Inertia Force vs. Torque F=ma   = I  Mass vs. Moment of Inertia mass   mR 2

18. Physics 218, Lecture IXX18 Two weights on a bar Find the moment of inertia for the two different Axes middle

19. Physics 218, Lecture IXX19 Spherical Heavy Pulley A heavy pulley, with radius R, starts at rest. We pull on an attached rope with a constant force F T. It accelerates to final angular speed  in time t. What is the moment of Inertia? R

20. Physics 218, Lecture IXX20 Less Spherical Heavy Pulley A heavy pulley, with radius R, starts at rest. We pull on an attached rope with constant force F T. It accelerates to final angular speed  in time t. A better estimate takes into account that there is friction in the system. This gives a torque (due to the axel) we’ll call this  fric. What is this better estimate of the moment of Inertia? R

21. Physics 218, Lecture IXX21 Pulley and Bucket A heavy pulley, with radius R, and known moment of inertia I starts at rest. We attach it to a bucket with mass m. The friction torque is  fric. Find the angular acceleration 

22. Physics 218, Lecture IXX22 Rotating Rod A uniform rod of mass m, length l, and moment of inertia I = ml 2 /3 rotates around a pivot. It is held horizontally and released. Find the angular acceleration  and the linear acceleration a at the end. Where, along the rod, is a = g?

23. Physics 218, Lecture IXX23 Next Time The rest of Chapter 10 –More on angular “Stuff” –Angular Momentum –Energy Next lecture will be the last topics on Exam 3. NEW EXAM DATE FOR Exam 3!!! Now Tuesday Nov 26 th

24. Physics 218, Lecture IXX24 Moments of Inertia